To observe the behavior for high-dimensional output regressions, we then consider the super-resolution task \({\mathbf {q}}_{\rm HR}={\cal F}({\mathbf {q}}_{\rm LR})\)  of two-dimensional cylinder wake.
Super-resolution analysis, originally developed in the field of image processing, aims to estimate high-resolution data from its low-resolution counterpart.
The idea had been applied to the fluid flow data by Fukami et al. [1]} in 2019.
The similar idea can also be applied to the universal closure modeling for LES and RANS [2]}, [3]}.
Moreover, considering that the low-resolution data corresponds to sparse sensor measurements, it can be applied to a global field reconstruction task from the limited data [4]}, [5]}.
These applications also encourage us to obtain detailed information of the weather or ocean data [6]}, which is crucial for disaster prevention.
Here, the low-resolution data \(\mathbf {q}_{\rm LR}\)  are generated by average pooling operation for original DNS data \(\mathbf {q}_{\rm HR}\)  to become 1/8 resolution of the original data.
